This question has come up before. My answer goes like this.
The universe we live in is 4 dimensional, 3 of length and one of time, and has a curious property, causality travels at the same rate in any direction in these 4 dimensions. Imagine you are standing still (wrt some inertial frame of reference.) Your ability to affect things in the future is constrained to propagate no faster than the speed of causality. Something you do now can only affect things a minute into the future once your action has propagated for one minute. You can’t have something you do now affecting something 10 minutes in the future propagate for only one minute. It can’t reach that future time. Set an alarm clock to ring in a minute’s time. The alarm clock’s state travels into the future a no faster than the maximum rate, and your future self sees the alarm clock ring in one minute. If you want to see what the world looks like in 100 years time, you must wait 100 years. Thus we know that causality propagates at one time unit per time unit, or for use mere Earthlings, one second per second.
But what if things moving?
How do we measure movement? Speed is distance per unit time. So we need to define a distance metric. As Chronos points out above, it makes no sense to use different units for different dimensions. We don’t measure height in inches and length in centimetres. The most obvious unit of length is the second. The basic unit of length is how far causality can travel in one second. Something is some distance from you. What is the shortest possible time something you do now affect that other object? If that object is 10 length units away from you, there is nothing you can do to have what you do now affect that object in less than 10 time units. Causality only travels at 1 unit per unit. If the object is 10 seconds away, it will take a minimum of 10 seconds to affect it. And you can have a mix of travel in time and in space. If you are travelling at some very fast speed you will discover that you are only able to travel of the speed of causality in the mix of time and spatial dimensions. The apparent speed in each dimension can be worked out with nothing more complex than Pythagoras’ theorem.
So how fast is causality? Clearly, in the only sensible units - it is 1. No dimensions, just 1.
Given we have defined the time unit to be one second, our unit of length is one causality second. This turns out to be an inconvenient number, being not too far off from the distance to the moon. And we didn’t know the speed of causality until much later than when we needed to measure lengths. (We missed by a few thousand years.) So we invented all manner of length units that were a bit more convenient. Cubits, yards, feet, metres, furlongs, rods, chains, miles, nautical miles, and so on. We could use seconds. As noted earlier, one nanosecond is pretty close to one foot.*
So what about the speed of light. Well, for a host of interesting reasons, it turns out that if you have no mass, you can’t travel in the time dimension, and can only travel in the spatial dimensions. But remember, the universe constrains us so that we can only travel at the speed of causality. If you are not travelling in time, you must be travelling at the speed of causality in space only. So light travels at this speed.
And, behold, we measure light to be travelling at the speed of causality in space. And in fundamental units, its speed is 1. If we used feet, its speed would come out at about one billion feet per second.
So how do we define our earthly units of measure? Well the metre was 1/10,000,000 of the distance from the pole to the equator on the meridian that runs through Paris. Not a particularly happy definition, and one that needed work. So they made a metal rod with some inscribed marks. Still not great. Now we define it in terms of time. We need a very accurate clock, and that clock is essentially an atomic clock. A Caesium atom emits energy with a very precise period. We define how many periods of a carefully defined description of exactly which energy emission we are using, and use that time period times the speed of causality to define the metre. Since rather conveniently light travels at the speed of causality, and the energy emission we are concerned with is light, we can measure not simply the time period, but count the number of wavelengths. And so we get the metre.
So why does the emission from the Caesium atom have this nice property we can measure, and this particular value? Well it is governed by some other laws of nature, and some other physical constants. And a key one of those for these purposes is the fine structure constant. Why does the fine structure constant have the value it does? We have no idea, but as noted above, we should be eternally grateful that it does.
- Whilst writing this I had the inspiration to initiate up a Kickstarter project to make a one nanosecond ruler. There are companies that make steel rules that will do custom rulers. (usually just with your company logo on etc) but it is just a matter of defining an etching pattern. A one nanosecond ruler would fit on the same blank as used for a one foot ruler. But rather than inches and fractions, the ruler measures exactly one nanosecond, and is divided in to 10 sub divisions, of 01. nanoseconds each, with further divisions beneath. Close to useless, but makes an important point. Maybe someone has already done this. I would buy one.
